If you look at the CO2 forcing above it looks pretty linear, but how about the total radiative forcing, because, our new hero's are claiming that.......greenhouse gas forcing, global temperature and solar irradiance are not polynomially cointegrated and AGW is refuted.

He also stressed that although one could in principle ˜squeeze™ information of exponential complexity into polynomially many quantum states, the real problem lay in the efficient retrieval of this information.

We observe that a simple formulation gives rise to systems at least as strong as Frege --- yielding a semantic way to define a Cook-Reckhow (i.e., polynomially verifiable) algebraic analogue of Frege proofs, different from that given in [BIKPRS96, GH03].

But Plancherel's theorem shows that there can only be polynomially many such large Fourier coefficients, so by the pigeonhole principle, is equal to a constant for a polynomially dense set of x, and the claim follows.

The second condition essentially means that the sequence should grow faster than any power of, as seems quite natural, then we find that the sequence grows at most polynomially (since the biggest we can get is at powers of 2, and to be a "constant" that tends to infinity.